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Description

Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field.

Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve.

This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.

Table of Contents

Preface
Some Applications of Functional Analysis to Analysis, Particularly to Nonlinear Integral Equations
The Differentiation and Integration of Nonlinear Operators
Differentiability and Related Properties of Nonlinear Operators: Some Aspects of the Role of Differentials in Nonlinear Functional Analysis
Generalized Inverses, Normal Solvability, and Iteration for Singular Operator Equations
On Polynomial Operators and Equations
Applications and Methods for the Minimization of Functionals
Toward a Unified Convergence Theory for Newton-Like Methods
Operator Solutions of Nonlinear Equations in Optimal Control Problems
Complementary Variational Principles
Index

About the Editor

Louis B. Rall

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